The principles of classical mechanics

The study of classical mechanics starts with Newton’s laws (principles) of motion. These laws are considered the foundation of classical mechanics. Newton’s laws are verified by experiments but they can not be demonstrated theoretically (mathematically).

Newton’s first law of motion

An object keeps its state as long as there is no force which acts upon it. The state of the body can be either stationary or moving with constant speed.

This law can be understood easily by analyzing the image above, where the letters mean:

A: a stationary object will remain stationary…
B: until an unbalanced force will act on it.
C: a moving object, will continue to move with constant speed…
D: until an unbalanced force will act on it.

Newton’s first law can be summarized as: an object with a mass will maintain its status quo, unless there is a force which will act on it.

Newton’s first law is also know as the principle of inertia.

Newton’s second law of motion

For a given body with mass, the resultant force F [N] acting on the body is equal with the product between the mass m [kg] and the body’s acceleration a [m/s²].

\[\bbox[#FFFF9D]{F = m \cdot a}\]

Force is defined as the change in time of the momentum p [kgm/s]:

\[p = m \cdot v\] \[F = \frac{dp}{dt} = \frac{d(mv)}{dt}=m \frac{dv}{dt} = ma\]

From Newton’s second law of motion we can deduce that the acceleration of a body in motion is directly proportional with the sum of forces acting on it and inversely proportional with its mass.

\[a = \frac{F}{m}\]

Newton’s second law is also know as the principle of force’s action.

Newton’s third law of motion

If a given body exerts a force on a second body, the second body will exert in the same time a force equal in magnitude and opposite in direction on the first body.

Newton’s second law can be summarized as: for each action there is a reaction.

\[G – N = 0\] \[\bbox[#FFFF9D]{G = N}\]

Newton’s second law is also known as the principle of action and reaction.

All Newton’s laws of motion are defining the force from three different perspectives: the first law defines the impact of a force on a body (qualitative definition), the second law defines the value of the force (quantitative definition), and the third law states that a single isolated force can not exist.

Parallelogram Law of Force Addition

This principle is not part of Newton’s laws of motion but it’s also a foundation law for classical mechanics. The parallelogram law of force addition states that: if upon a point P act simultaneously two forces F₁ and F₂, their effect is the same as if upon the point was acting a single force F equal in magnitude and direction with the diagonal of the parallelogram formed by the two forces.

These four principles will serve as a basis for upcoming mechanics tutorials so understanding them will help building solid knowledge of classical (Newtonian) mechanics.

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